Compression and Conditional Effects: A Product Term Is Essential When Using Logistic Regression to Test for Interaction*

Previous research in political methodology argues that researchers do not need to include a product term in a logistic regression model to test for interaction if they suspect interaction due to compression alone. I disagree with this claim and offer analytical arguments and simulation evidence that when researchers incorrectly theorize interaction due to compression, models without a product term bias the researcher, sometimes heavily, toward finding interaction. However, simulation studies also show that models with a product term fit a broad range of non-interactive relationships surprisingly well, enabling analysts to remove most of the bias toward finding interaction by simply including a product term.

Carlisle Rainey is Assistant Professor of Political Science in the Texas A&M University, 2010 Allen Building, College Station, TX 77843 (crainey@tamu.edu). The author thanks Kenneth Benoit, Bill Berry, Scott Clifford, Justin Esarey, and two anonymous reviewers for helpful comments on earlier versions of this manuscript. The author also thanks John Oneal and Bruce Russet for making their data available, the Center for Computational Research at the University at Buffalo for providing support for the simulations. Code and data necessary to replicate the simulations and empirical analysis is available at http://www.carlislerainey.com/research and at http://thedata.harvard.edu/dvn/dv/PSRM. To view supplementary material for this article, please visit http://10.1017/psrm.2015.59

Footnotes

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Carlisle Rainey is Assistant Professor of Political Science in the Texas A&M University, 2010 Allen Building, College Station, TX 77843 (crainey@tamu.edu). The author thanks Kenneth Benoit, Bill Berry, Scott Clifford, Justin Esarey, and two anonymous reviewers for helpful comments on earlier versions of this manuscript. The author also thanks John Oneal and Bruce Russet for making their data available, the Center for Computational Research at the University at Buffalo for providing support for the simulations. Code and data necessary to replicate the simulations and empirical analysis is available at http://www.carlislerainey.com/research and at http://thedata.harvard.edu/dvn/dv/PSRM. To view supplementary material for this article, please visit http://10.1017/psrm.2015.59

Berry, Frances Stokes, and Berry, William D.. 1990. ‘State Lottery Adoptions as Policy Innovations: An Event History Analysis’. American Political Science Review84(2):395–415.

Berry, Frances Stokes, and Berry, William D.. 1991. ‘Specifying a Model of State Policy Innovation’. American Political Science Review85(2):573–579.

Berry, William, DeMeritt, Jacqueline H. R., and Esarey, Justin. 2010. ‘Testing for Interaction in Binary Logit and Probit Models: Is a Product Term Essential?’. American Journal of Political Science54:248–266.

Hanmer, Michael, and Kalkan, Kerem Ozan. 2013. ‘Behind the Curve: Clarifying the Best Approach to Calculating Predicted Probabilities and Marginal Effects from Limited Dependent Variable Models’. American Journal of Political Science57(1):263–277.